Lab Assignment 5

Correlation and Regression Analysis

Due on Friday by 5PM

One Submission for Each Team (Not All Team Members)

(Upload your work on Blackboard Dropbox under Assignment)

Import "Recoded_Taste_Test_Data.xlsx" into SPSS and

Use RED color to mark right answer in parenthesis or replace ??? with the numbers from SPSS output

1. Conduct correlation analysis.

(1) Draw scatterplots between Prob and variables such as New_Price, and New_Image, Taste. [SPSS Hint: Use Graphs>Chart Builer>Scatter/Dot command]

Copy and Paste SPSS output below

a. Scatterplot between Prob and New_Price

b. Scatterplot between Prob and New_Image

c. Scatterplot between Prob and Taste

(2) Examine the correlations between Prob and variables such as New_Price, New_Image, Taste, and DUMMY_Gender [Hint: use Pearson Correlation and examine the 2-tailed t-test and associated p-value.] [SPSS Hint: Use Analyze>Correlate>Bivariate command

Copy and Paste SPSS output below

Instruction: For each correlation coefficient, you need to

Specify the correlation coefficient

Construct the null and alternative hypotheses

Specify which test you utilize and Whether it is a one-tailed or two-tailed test

Draw the conclusion

oDetermine whether or not your hypotheses are supported based on the P-value associated with your test => Whether the correlation coefficient is statistically significant

oSpecify what you learn from these correlations (underlying form, significance, direction, strength)

Correlation between Prob and New_Price

oThe correlation coefficient is ???

oH₀: The correlation = ???

Ha: The correlation ? ???

oT test and two tailed test (Since we can reject the null hypothesis for a test statistic which is much smaller or larger than 0, there are two rejection regions)

oSince the corresponding p-value is less than 0.1, the correlation is statistically significant at significance level 10% (0.1)

oThere is a (positive vs. negative)correlation between these two variables and the correlation is weak

Correlation between Prob and New_Image

oThe correlation coefficient is ???

oH₀: The correlation = ???

Ha: The correlation ? ???

oT test and two tailed test (Since we can reject the null hypothesis for a test statistic which is much smaller or larger than 0, there are two rejection regions)

oSince the corresponding p-value is larger than 0.05, the correlation is statistically (significant vs. insignificant) at significance level 5% (0.05)

oSince the correlation is statistically NOT significant, we do not make any interpretation

Correlation between Prob and Taste

oThe correlation coefficient is ???

oH₀: The correlation = ???

Ha: The correlation ? ???

oT test and two tailed test (Since we can reject the null hypothesis for a test statistic which is much smaller or larger than 0, there are two rejection regions)

oSince the corresponding p-value is less than 0.05, the correlation is statistically significant at significance level 5% (0.05)

oThere is a (positive vs. negative) correlation between these two variables and the correlation is moderate

Correlation between Prob and DUMMY_Gender

oThe correlation coefficient is ???

oH₀: The correlation = ???

Ha: The correlation ? ???

oT test and two tailed test (Since we can reject the null hypothesis for a test statistic which is much smaller or larger than 0, there are two rejection regions)

oSince the corresponding p-value is less than 0.05, the correlation is statistically (significant vs. insignificant) at significance level 5% (0.05)

oThere is a (positive vs. negative)correlation between these two variables and the correlation is weak

2. Conduct Regression Analysis

(1) Run a simple regression of the Prob variable (dependent/response variable) on the Taste variable (independent/explanatory variable). [SPSS Hint: Use Analyze>Regression>Linear command]

Copy and Paste SPSS output below

(2) Construct the equation for this simple regression.

???=?₀ + ?₁??? + ?

(3) Which variables are statistically significant?

a. For the intercept parameter (?₀),

Intercept coefficient estimate is ???

H₀: The intercept coefficient parameter (?₀) = ??? (the intercept coefficient parameter is statistically insignificant)

Ha: The intercept coefficient parameter (?₀) ? ??? (the intercept coefficient parameter is statistically significant)

T-test & Two-tailed test (the null hypothesis includes =. So, we can reject the null hypothesis for a test statistic which is much smaller or larger than 0 => There are two rejection regions => A two-tailed test)

P-value (???) We (fail to reject vs. reject) the null hypothesis (H₀), and hence, we (accept vs. reject) the alternative (Ha) hypothesis (Research Question) => The research question that the intercept is statistically significant is (NOT supported vs. supported)

The intercept (?₀) is statistically (significant vs. insignificant) at significance level 5% (0.05)

b. For the coefficient parameter of the Taste variable (?₁),

Coefficient estimate for Taste is ???

H₀: The coefficient parameter for Taste (?₁) = ??? (this coefficient parameter is statistically insignificant)

Ha: The coefficient parameter for Taste (?₁) ? ??? (this coefficient parameter is statistically significant)

T-test & Two-tailed test (the null hypothesis includes =. So, we can reject the null hypothesis for a test statistic which is much smaller or larger than 0 => There are two rejection regions => A two-tailed test)

P-value (???) We (fail to reject vs. reject) the null hypothesis (H₀), and hence, we (accept vs. reject) the alternative (Ha) hypothesis (Research Question) => The research question that the Taste coefficient parameter (hence variable Taste) is statistically significant is (NOT supported vs. supported)

The coefficient parameter of Taste (?₁) (and thus, the Taste variable) is statistically (significant vs. insignificant) at significance level 5% (0.05).

(4) Interpret the coefficient of each parameter/variable.

The intercept estimate ( ) is ???, which means that the value of Prob is ??? when the value of Taste is zero.

The coefficient estimate for Taste ( ) is ???, which means that if taste goes up by 1, Prob (Probability or the likelihood or probability that you would purchase six or more bottles of Bravo (Delight) per month) will (increase vs. decrease) by ???, controlling for the other variables (such as Price, Image, and Gender).

(5) If you want to predict Prob with data from a new set of customers, what would be the equation you would use? What would be the predicted Prob score for a new customer whose taste score is 70?

Prob=?₀+ ?₁Taste + ?

=+ Taste

= ??? + ???*???

= ???

(6) Report Adjusted R-squared

???

3. Run a multiple regression of the Prob variable (dependent/response variable) on such variables as New_Price, New_Image, Taste, and DUMMY_Gender (independent/explanatory variables). [SPSS Hint: Use Analyze>Regression>Linear command]

Copy and Paste SPSS output below

(1) The equation for this multiple regression is as follows:

Prob=?₀ + ?₁New_Price + ?₂ New_Image + ?₃Taste + ?₄DUMMY_Gender + ?

(2) Which variables are statistically significant? For each coefficient parameter (i.e., the intercept parameter and coefficient parameters of variables), specify coefficient estimate, construct the null and alternative hypotheses, specify which test you utilize and whether it is a one-tailed or two-tailed test, determine whether or not your hypothesis is supported based on the p-value associated with your test, and draw the conclusion (the statistical significance of each coefficient parameter).

a. For the intercept parameter (?₀),

Intercept coefficient estimate is ???

H₀: The intercept coefficient parameter (?₀) = ??? (the intercept coefficient parameter is statistically insignificant)

Ha: The intercept coefficient parameter (?₀) ? ??? (the intercept coefficient parameter is statistically significant)

The null hypothesis includes =. So, we can reject the null hypothesis for a test statistic which is much smaller or larger than 0 => There are two rejection regions => (one-tailed test vs. two-tailed test)

ID Treat 1 Bravo 2 Bravo 3 Bravo 4 Bravo 5 Bravo 7 Bravo 8 Bravo 9 Bravo 10 Bravo 11 Bravo 12 Bravo 13 Bravo 14 Bravo 15 Bravo 16 Bravo 17 Bravo 18 Bravo 19 Bravo 20 Bravo 21 Bravo 22 Bravo 23 Bravo 24 Bravo 26 Bravo 27 Bravo 28 Bravo 29 Bravo 30 Bravo 31 Bravo 32 Bravo 33 Bravo 34 Bravo 35 Bravo 36 Bravo 37 Bravo 38 Bravo 39 Bravo 40 Bravo 41 Delight 42 Delight 43 Delight 44 Delight 45 Delight 46 Delight Gender Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Male Male Male Male Male Male Age Bottle 19 21 23 20 25 19 46 22 38 18 19 27 21 20 23 19 20 21 19 20 18 24 20 20 24 22 22 20 31 21 18 29 32 24 20 28 19 27 21 20 22 18 25 23 Day 0 0 2 12 0 0 36 18 6 12 0 24 10 18 12 24 0 0 12 0 0 0 12 0 2 12 0 18 6 0 0 12 0 6 0 6 0 0 12 6 42 0 0 10 Price Image Taste 0 Extremely Extremely 0 Extremely Not Sure 1 Not Sure Very Unimp 4 Very ImporVery Impor 0 Very UnimpSomewhat 0 Extremely Somewhat 5 Somewhat Extremely 4 Somewhat Not Sure 3 Extremely Very Unimp 4 Very ImporExtremely 0 Very UnimpVery Impor 5 Extremely Extremely 3 Extremely Very Unimp 4 Extremely Not Sure 3 Very ImporExtremely 5 Extremely Somewhat 0 Not Sure Not Sure 0 Extremely Extremely 4 Very UnimpExtremely 0 Extremely Very Impor 0 Extremely Not Sure 0 Not Sure Somewhat 5 Very ImporExtremely 0 Very UnimpNot Sure 1 Extremely Extremely 4 Not Sure Not Sure 0 Extremely Somewhat 6 Somewhat Somewhat 1 Very ImporSomewhat 0 Extremely Very Impor 0 Very ImporVery Unimp 7 Very UnimpVery Impor 0 Extremely Extremely 2 Very ImporExtremely 0 Very UnimpVery Unimp 3 Somewhat Somewhat 0 Extremely Very Unimp 0 Extremely Very Unimp 2 Not Sure Somewhat 3 Extremely Very Impor 6 Somewhat Somewhat 0 Very UnimpVery Impor 0 Extremely Somewhat 4 Very ImporVery Unimp Rank_A 48 90 50 65 62 56 72 62 35 60 60 64 70 54 40 58 66 70 58 53 70 59 67 62 65 72 85 66 58 64 65 69 85 70 61 63 65 71 35 38 46 52 40 41 5 1 4 4 2 2 1 3 5 2 1 2 2 3 3 3 2 1 2 4 2 3 1 3 2 3 1 4 2 2 3 1 2 1 3 3 2 2 5 4 4 2 3 3 48 Delight 49 Delight 50 Delight 51 Delight 52 Delight 53 Delight 54 Delight 55 Delight 57 Delight 58 Delight 59 Delight 60 Delight 61 Delight 62 Delight 63 Delight 64 Delight 65 Delight 66 Delight 67 Delight 68 Delight 69 Delight 70 Delight 71 Delight 73 Delight 74 Delight 75 Delight 76 Delight 77 Delight 78 Delight 79 Delight 80 Delight Male Male Male Male Male Male Male Male Male Male Male Male Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female 19 21 22 20 26 21 23 18 20 20 19 21 23 28 19 40 21 18 52 21 20 35 19 20 19 32 20 18 21 20 19 18 0 0 2 0 0 12 18 12 6 12 0 72 12 6 0 6 0 0 6 0 18 0 6 0 0 1 0 0 0 12 2 Not Sure Extremely 0 Extremely Somewhat 0 Extremely Not Sure 2 Somewhat Not Sure 0 Very ImporExtremely 0 Extremely Somewhat 3 Not Sure Extremely 3 Extremely Very Unimp 4 Very ImporVery Unimp 2 Very ImporExtremely 4 Very UnimpVery Impor 0 Extremely Very Impor 7 Extremely Very Unimp 4 Not Sure Very Impor 4 Somewhat Not Sure 0 Very ImporNot Sure 2 Very UnimpExtremely 0 Not Sure Somewhat 0 Extremely Very Impor 1 Somewhat Very Impor 0 Extremely Extremely 3 Extremely Extremely 0 Not Sure Not Sure 2 Very UnimpVery Impor 0 Extremely Extremely 0 Extremely Not Sure 1 Extremely Extremely 0 Not Sure Not Sure 0 Extremely Very Unimp 0 Very UnimpNot Sure 3 Very ImporSomewhat 36 44 80 42 39 40 38 28 42 34 25 35 85 95 90 85 77 81 79 87 50 87 90 60 30 80 78 92 86 96 87 2 4 1 2 3 3 4 5 2 4 5 4 2 1 3 1 1 3 2 1 5 2 1 3 5 2 3 1 1 1 4 Rank_B Rank_C 1 2 3 2 3 5 2 4 1 1 2 3 1 4 2 1 1 2 3 5 1 1 2 2 3 2 2 1 1 3 1 2 1 2 2 1 3 4 4 1 1 1 2 1 Rank_D 4 5 5 3 5 4 5 5 2 3 4 5 5 5 4 2 3 4 4 1 3 5 4 4 5 5 3 5 4 4 4 5 5 5 1 5 1 3 3 5 3 5 5 5 Rank_E 2 4 2 1 1 1 4 2 4 5 3 1 3 1 1 4 5 3 5 3 4 4 3 1 1 4 5 2 3 1 2 4 3 3 4 2 4 5 1 3 2 4 4 2 Prob 3 3 1 5 4 3 3 1 3 4 5 4 4 2 5 5 4 5 1 2 5 5 5 5 4 1 4 3 5 5 5 3 4 4 5 4 5 1 2 2 5 3 1 4 Choice New_TreatDUMMY_Ge New_PriceNew_Imag 20 3 1 0 1 7 100 3 1 0 7 4 15 3 1 0 4 6 30 Bravo (Deli 1 0 2 2 80 3 1 0 6 5 50 Bravo (Deli 1 0 1 5 75 3 1 0 5 1 50 3 1 0 3 4 03 1 0 7 6 20 3 1 0 2 1 50 3 1 0 6 2 80 3 1 0 7 1 90 Bravo (Deli 1 0 1 6 03 1 0 7 4 50 Bravo (Deli 1 0 2 7 20 3 1 0 7 3 100 Bravo (Deli 1 0 4 4 90 Bravo (Deli 1 0 1 7 50 3 1 0 6 1 50 3 1 1 7 2 70 3 1 1 7 4 20 3 1 1 4 5 100 Bravo (Deli 1 1 2 7 50 3 1 1 6 4 0 Bravo (Deli 1 1 1 7 20 3 1 1 4 4 90 Bravo (Deli 1 1 1 3 03 1 1 5 3 90 Bravo (Deli 1 1 2 5 75 3 1 1 7 2 03 1 1 2 6 100 3 1 1 6 2 100 Bravo (Deli 1 1 1 7 50 Bravo (Deli 1 1 2 7 20 3 1 1 6 6 03 1 1 5 5 90 3 1 1 7 6 50 Bravo (Deli 1 1 1 6 03 2 0 4 3 10 3 2 0 7 2 03 2 0 3 3 50 3 2 0 6 2 50 Bravo (Deli 2 0 1 3 75 Bravo (Deli 2 0 2 6 1 2 2 1 2 1 2 4 3 3 1 2 1 3 2 3 2 1 1 3 2 1 4 1 2 1 2 3 2 2 1 4 5 3 4 1 5 5 2 4 5 4 5 3 5 5 4 3 5 4 4 4 3 5 4 3 5 4 4 5 3 5 5 1 4 3 5 4 1 3 1 2 2 1 5 2 1 5 4 2 3 2 1 5 2 2 1 4 5 2 3 4 3 3 3 5 5 4 2 3 1 5 1 3 3 4 4 4 2 5 4 5 5 3 4 3 5 4 4 1 5 4 5 2 100 3 03 100 Bravo (Deli 50 3 0 Bravo (Deli 03 10 3 03 50 Bravo (Deli 03 03 10 3 100 Bravo (Deli 90 Bravo (Deli 03 100 3 50 3 50 3 75 Bravo (Deli 90 Bravo (Deli 03 50 Bravo (Deli 100 Bravo (Deli 50 Bravo (Deli 03 100 Bravo (Deli 50 3 90 Bravo (Deli 75 Bravo (Deli 100 3 03 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 7 1 5 2 7 4 1 2 2 6 7 1 4 5 2 6 4 1 3 7 1 4 6 7 1 7 4 1 6 2 7 3 4 4 7 3 1 6 6 7 2 2 6 2 4 4 7 3 2 2 1 7 4 2 7 4 1 4 6 4 3 New_ChoicAge_Month 1 228 1 252 1 276 2 240 1 300 2 228 1 552 1 264 1 456 1 216 1 228 1 324 2 252 1 240 2 276 1 228 2 240 2 252 1 228 1 240 1 216 1 288 2 240 1 240 2 288 1 264 2 264 1 240 2 372 1 252 1 216 1 348 2 384 2 288 1 240 1 336 1 228 2 324 1 252 1 240 1 264 1 216 2 300 2 276 1 1 2 1 2 1 1 1 2 1 1 1 2 2 1 1 1 1 2 2 1 2 2 2 1 2 1 2 2 1 1 228 252 264 240 312 252 276 216 240 240 228 252 276 336 228 480 252 216 624 252 240 420 228 240 228 384 240 216 252 240 228